An open organ pipe of length l is sounded together with another open organ pipe of length l + x in their fundamental tones. Speed of sound in air is v. The beat frequency heard will be (x ≪ l)
vx2l2
Beat frequency =f1−f2
=v2l−v1(l+x)=v21[1−(1+x1)−1]
=v2l[1−1+x1]=vx2l2